Regents Exam Questions A2.A.75: Law of Sines – The Ambiguous Case 2
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Name: __________________________________
A2.A.75: Law of Sines - The Ambiguous Case: Determine the solution(s) from
the SSA situation (ambiguous case)
1 In
,
,
the nearest tenth?
, and
. What are the two possible values for
2 How many distinct triangles can be formed if
,
, and
3 How many distinct triangles can be formed if
, side
5 If the measure of
constucted?
6 In
,
,
, and
these measurements?
,
, and
?
, and side
4 What is the total number of distinct triangles that can be constructed if
and
?
, to
?
,
,
, how many different triangles can be
. How many distinct triangles can be drawn given
7 How many distinct triangles can be constructed if
?
, side
, and side
8 Sam is designing a triangular piece for a metal sculpture. He tells Martha that two of the
sides of the piece are 40 inches and 15 inches, and the angle opposite the 40-inch side
measures 120°. Martha decides to sketch the piece that Sam described. How many
different triangles can she sketch that match Sam’s description?
9 An architect commissions a contractor to produce a triangular window. The architect
describes the window as
, where
,
inches, and
inches.
How many distinct triangles can the contractor construct using these dimensions?
10 Sam needs to cut a triangle out of a sheet of paper. The only requirements that Sam must
follow are that one of the angles must be 60°, the side opposite the 60° angle must be 40
centimeters, and one of the other sides must be 15 centimeters. How many different
triangles can Sam make?
Regents Exam Questions A2.A.75: Law of Sines – The Ambiguous Case 2
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1 ANS:
78.3 and 101.7
REF: 081006a2
2 ANS:
2
.
REF: 011113a2
3 ANS:
2
REF: 080414b
4 ANS:
2
REF: 080519b
5 ANS:
Regents Exam Questions A2.A.75: Law of Sines – The Ambiguous Case 2
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2
.
REF: 061011b
6 ANS:
2
REF: 011419a2
7 ANS:
none
REF: 011523a2
8 ANS:
1
The triangle has an obtuse angle of 120°, and may not have a second obtuse angle. Check if one triangle
is possible.
REF: 060416b
9 ANS:
2
Regents Exam Questions A2.A.75: Law of Sines – The Ambiguous Case 2
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REF: 080311b
10 ANS:
1
REF: 060620b